Underlying mechanism of the topographic factor scale effect in soil erosion equations

The topographic factor (LS factor), derived from the multiplication of the slope length (L) and slope steepness (S) factors, is a vital parameter in soil erosion models. Generated from the digital elevation model (DEM), the LS factor always varies with the changing DEM resolution, i.e., the LS factor scale effect. Previous studies have found the phenomenon of the LS factor scale effect, but the underlying causes of this phenomenon has not been well explored. Therefore, how the DEM resolution affects the LS factor and how the scale effect of the L and S factors influence the LS factor scale effect remains unclear. To address these problems, we collected 20 watersheds from the Guangdong Province with different topographic reliefs, and compared the corresponding L, S and LS factors at 10-m and 30-m resolution DEMs. Our results indicate that the S factor, heavily influenced by slope underestimation in coarse-resolution DEMs, makes a difference in the LS factor scale effect. In addition, the LS factor scale effect becomes less significant with increasing reliefs, suggesting the possibility of using 30-m DEM for LS calculation in rugged terrains. Our findings on the underlying mechanisms of the LS factor scale effect help to identify the uncertainty in the LS factor estimation, thereby enhancing the accuracy of soil erosion assessment, particularly in regions with different topographic characteristics and contribute to more effective soil conservation strategies and decision-making.